Determining which integer is closest to the kth root of n without using floating point arithmetic?

Suppose that I want to compute ^k√n rounded to the nearest integer, where n and k are nonnegative integers. Using binary search, I can find an integer a such that

a^k ≤ n < (a+1)^k.

This means that either a or a+1 is the kth root of n rounded to the nearest integer. However, I'm not sure how to determine which one it is without doing some calculations that involve floating-point arithmetic.

Given the values of a, n, and k, is there a way to determine the kth root of n rounded to the nearest integer without doing any floating-point calculations?

Thanks!